There are a few fundamental realities about the Universe like its origin, its past, and its present state that are mindboggling. On the forefront of this list is the Big Bang theory and the idea that the Universe began 13.8 billion years ago full of matter and radiation, and the components that would eventually evolve into stars, galaxies, planets, and living creatures. Now the big question is how far away can we see? It is usually presumed that in a Universe limited by the speed of light, our reach would be restricted to 13.8 billion light-years i.e. the known age of the Universe multiplied by the speed of light. But this value is far too small to be the correct answer. In actuality, we can see an amazing 46 billion light years in all directions making a total diameter of 92 billion light years.
There appear to be three intuitive ways this extended diameter is possible-
Stuff is everywhere, light travels at the speed of light: This is the “default” mode. Consider a Universe full of stars and galaxies everywhere possible, and these stars and galaxies began forming pretty close to the very beginning of everything. As light travels in a straight line at the speed of light, the longer we wait, the farther we can see. So after 13.8 billion years, you’d expect to be able to see back almost 13.8 billion light-years, deducting only the time it took for stars and galaxies to form after the Big Bang.
Stuff is everywhere, light moves at the constant c, and everything can move through space: This complicates the scenario but not only is there a number of entities that emits light, but these light-emitting objects can move relative to one another. Since they can move up to nearly the speed of light, by the rules of special relativity, while the light moves towards you at the speed of light, you can visualize twice as far as that possible in the first case. Perhaps the same objects could now be as far as 27.6 billion light-years away, assuming their light just reaches us now and they speed away from us at nearly the speed of light.
Stuff is everywhere, light moves at c, stars, and galaxies move, the Universe is expanding: This last scenario is the counterintuitive one that most people struggle with. Space is full of matter, which rapidly bunches into stars, galaxies and even larger structures. The produced light moves at constant c, the speed of light in vacuum. All existing matter moves through space, mostly owing to the mutual gravitational attraction of different over dense and underdense regions on one another. All of this is true and similar to the second scenario. The added complication is that space itself is expanding.
When you gaze at a distant galaxy and it seems redder than normal, the common understanding was that the galaxy is red as it’s moving away from us, and hence the light shifted towards the longer i.e. redder wavelengths the same way as a siren moving away from you has its sound moved to longer wavelengths and lower pitches. General Relativity adds that extra element in the theory of space expanding. As the Universe expands stretching the fabric of space, the individual light waves in that space see their wavelengths stretch as well!
It might seem impossible to tell these two effects apart. But there is a relationship that exists between the redshift and consequently the wavelength and the observable brightness of the galaxy which is a function of the distance.
In a non-expanding Universe, the maximum observable distance is twice the age of the Universe in light years i.e. 27.6 billion light years. But in our expanding Universe, we’ve already observed galaxies farther away than that.
So how far can we really see in any direction? In a Universe with no dark energy at all, the farthest objects like stars, galaxies, the residual glow from the Big Bang, etc., would be restricted to 41.4 billion light years. But in a Universe like ours with dark energy, the restriction gets pushed out to a greater number to 46 billion light years to account for the observed dark energy our cosmos possesses.
Cumulatively, this means that the distance visible across the Universe, from one distant end to the other, is 92 billion light years. And as it continues to expand, if we left today at the speed of light, we could only cover about a third of the way across it around 3% of its volume. This implies that the Universe’s expansion and the presence of dark energy make 97% of the observable Universe is already unreachable, even at the speed of light.
Although 92 billion light years seems like a large number for a 13.8-billion-year-old Universe, it’s the appropriate figure for the present-day Universe, full of matter, radiation, dark energy, and conforming to the laws of General Relativity. The Universe appears as big as it is to our eyes due to the fact that space itself is expanding, and new space is constantly created in between the bound galaxies, groups and clusters in the cosmos.